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arxiv: 0901.1592 · v3 · submitted 2009-01-12 · ✦ hep-th

Poisson-Lie T-dual sigma models on supermanifolds

classification ✦ hep-th
keywords poisson-liemodelssuperbosonicfermionicfieldsmodelsigma
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We investigate Poisson-Lie symmetry for T-dual sigma models on supermanifolds in general and on Lie supergroups in particular. We show that the integrability condition on this super Poisson-Lie symmetry is equivalent to the super Jacobi identities of the Lie super-bialgebras. As examples we consider models related to four dimensional Lie super-bialgebras $((2A1,1 + 2A)^1, D10_p=1/2)$ and $((2A1,1 + 2A)^1, I)$. Then generally it is shown that for Abelian case (g, I) the super Poisson-Lie T-duality transforms the role of fermionic (bosonic) fields in the model to bosonic (fermionic) fields on the dual model and vice versa.

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